Question: Let p(x) = x' + x2 - x - 1, q(x) = x2 - 1, and r(x) = 2 x3 - 2 x be three

Let p(x) = x' + x2 - x - 1, q(x) = x2 - 1, and r(x) = 2 x3 - 2 x be three vectors in P3(R): real polynomials of degree at most 3. Let W = (p(x), q(x), r(x)}. a) Is W a linearly independent set? Explain! b) Find a basis and the dimension for span( W)

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